Abstract
Second harmonic generation (SHG) can be used as a technique for controlling the spatial mode structure of optical beams. We demonstrate experimentally the generation of higherorder spatial modes, and the possibility to use nonlinear phase matching as a predictable and robust technique for the conversion of transverse electric modes of the second harmonic output. The details of this effect are well described by our wave propagation models, which include mode dependent phase shifts. This is, to our knowledge, the first detailed study of spatial mode conversion in SHG. We discuss potential applications of this effect.
© 2007 Optical Society of America
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References
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 Year
 
 Author
 
 Publication
 V. KhokhlovRadiotek. Electron 6, 1116–1130 (1961).
 P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]  R.W. Boyd, Nonlinear Optics, (Academic Press, 1992).
 G. Gurzadian, D.N. Nikogosian, and V.G. Dmitriev, Handbook of Nonlinear Optical Crystals, (Springer, 2006).

R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref] [PubMed] 
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]  A.E. Siegman, Lasers, (University Science, Mill Valley California, 1986).
 G.D. Boyd and D.A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys., 39, 3597–3639 (1968).
[Crossref] 
J.T. Lue and C.J. Sun, “Limiting factors for parametric generation with focused highorder transverse and multilongitudinalmode lasers,” J. Opt. Soc. Am. B 4, 1958–1963 (1987).
[Crossref]  L.G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).
 R.W. Boyd, “Intuitive Explanation of the Phase Anomaly of Focused Light Beams,” J. Opt. Soc. Am 70, 877–880 (1980).
[Crossref]  M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]  V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
 T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]  S. Sheng and A. E. Siegman, “Nonlinearoptical calculations using fasttransform methods: Secondharmonic generation with depletion and diffraction,” Phys. Rev. A, 21, 599–606 (1980).
[Crossref]  N. Lastzkaet. al., arXiv.org:physics/0611257, (2006).
 M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).

J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref] [PubMed]  H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref] 
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref] [PubMed] 
W.M. Lee, X. Yuan, and D. Tang, “Optical tweezers with multiple optical forces using doublehologram interference,” Opt. Express, 11, 199–207 (2002).
[Crossref]
2007 (1)
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
2006 (1)
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
2005 (1)
T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]
2004 (1)
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
2002 (1)
W.M. Lee, X. Yuan, and D. Tang, “Optical tweezers with multiple optical forces using doublehologram interference,” Opt. Express, 11, 199–207 (2002).
[Crossref]
1995 (2)
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]
H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref]
1994 (1)
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
1987 (1)
J.T. Lue and C.J. Sun, “Limiting factors for parametric generation with focused highorder transverse and multilongitudinalmode lasers,” J. Opt. Soc. Am. B 4, 1958–1963 (1987).
[Crossref]
1986 (1)
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
1980 (2)
S. Sheng and A. E. Siegman, “Nonlinearoptical calculations using fasttransform methods: Secondharmonic generation with depletion and diffraction,” Phys. Rev. A, 21, 599–606 (1980).
[Crossref]
R.W. Boyd, “Intuitive Explanation of the Phase Anomaly of Focused Light Beams,” J. Opt. Soc. Am 70, 877–880 (1980).
[Crossref]
1968 (1)
G.D. Boyd and D.A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys., 39, 3597–3639 (1968).
[Crossref]
1961 (2)
V. KhokhlovRadiotek. Electron 6, 1116–1130 (1961).
P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]
1890 (1)
L.G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).
Ashkin, A.
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
Bachor, HA.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
Bjorkholm, J. E.
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
Boyd, G.D.
G.D. Boyd and D.A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys., 39, 3597–3639 (1968).
[Crossref]
Boyd, R.W.
R.W. Boyd, “Intuitive Explanation of the Phase Anomaly of Focused Light Beams,” J. Opt. Soc. Am 70, 877–880 (1980).
[Crossref]
R.W. Boyd, Nonlinear Optics, (Academic Press, 1992).
Breitenbach, G.
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]
Buchhave, P.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
Chu, Steven
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
Delaubert, V.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
Dmitriev, V.G.
G. Gurzadian, D.N. Nikogosian, and V.G. Dmitriev, Handbook of Nonlinear Optical Crystals, (Springer, 2006).
Dziedzic, J. M.
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
Fabre, C.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
Fejer, M.M.
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
Franken, P.A.
P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]
Friese, M.E.J.
H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref]
Gouy, L.G.
L.G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).
Gurzadian, G.
G. Gurzadian, D.N. Nikogosian, and V.G. Dmitriev, Handbook of Nonlinear Optical Crystals, (Springer, 2006).
Harb, C.C.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
He, H.
H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref]
Heckenberg, N.R.
H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref]
Henking, R.
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
Hill, A.E.
P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]
Huang, J.
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
Janousek, J.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
Kan, H
T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]
Kasamatsu, T.
T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]
Khokhlov, V.
V. KhokhlovRadiotek. Electron 6, 1116–1130 (1961).
Kleinman, D.A.
G.D. Boyd and D.A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys., 39, 3597–3639 (1968).
[Crossref]
Kubomura, H.
T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]
Kurz, J.R.
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
Kurz, P.
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
Lam, P.K.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
Lassen, M.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
Lastzka, N.
N. Lastzkaet. al., arXiv.org:physics/0611257, (2006).
Lee, W.M.
W.M. Lee, X. Yuan, and D. Tang, “Optical tweezers with multiple optical forces using doublehologram interference,” Opt. Express, 11, 199–207 (2002).
[Crossref]
Lue, J.T.
J.T. Lue and C.J. Sun, “Limiting factors for parametric generation with focused highorder transverse and multilongitudinalmode lasers,” J. Opt. Soc. Am. B 4, 1958–1963 (1987).
[Crossref]
Mlynek, J.
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
Nikogosian, D.N.
G. Gurzadian, D.N. Nikogosian, and V.G. Dmitriev, Handbook of Nonlinear Optical Crystals, (Springer, 2006).
Paschotta, R.
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
Peters, C.W.
P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]
Pulford, D.R.N.
V. Delaubert, M. Lassen, D.R.N. Pulford, HA. Bachor, and C.C. Harb, Generalized BoydKleinman Calculation of High Order Transverse Modes Second Harmonic Generation, To be submitted (2007).
RubinszteinDunlop, H.
H. He, M.E.J. Friese, N.R. Heckenberg, and H. RubinszteinDunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with phase singularity,” Phys. Rev. Lett. 75, 826829–826833 (1995).
[Crossref]
Saida, T.
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
Schiller, S.
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]
R. Paschotta, P. Kurz, R. Henking, S. Schiller, and J. Mlynek, “82% efficient continuouswave frequency doubling of 1.06 mm with a monolithic MgO:LiNbO3 resonator,” Opt. Lett. 19, 1325–1327 (1994).
[Crossref]
[PubMed]
Sheng, S.
S. Sheng and A. E. Siegman, “Nonlinearoptical calculations using fasttransform methods: Secondharmonic generation with depletion and diffraction,” Phys. Rev. A, 21, 599–606 (1980).
[Crossref]
Siegman, A. E.
S. Sheng and A. E. Siegman, “Nonlinearoptical calculations using fasttransform methods: Secondharmonic generation with depletion and diffraction,” Phys. Rev. A, 21, 599–606 (1980).
[Crossref]
Siegman, A.E.
A.E. Siegman, Lasers, (University Science, Mill Valley California, 1986).
Sun, C.J.
J.T. Lue and C.J. Sun, “Limiting factors for parametric generation with focused highorder transverse and multilongitudinalmode lasers,” J. Opt. Soc. Am. B 4, 1958–1963 (1987).
[Crossref]
Tang, D.
W.M. Lee, X. Yuan, and D. Tang, “Optical tweezers with multiple optical forces using doublehologram interference,” Opt. Express, 11, 199–207 (2002).
[Crossref]
Treps, N.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
Wagner, K.
M. Lassen, V. Delaubert, J. Janousek, K. Wagner, HA. Bachor, P.K. Lam, N. Treps, P. Buchhave, C. Fabre, and C.C. Harb, “Tools for spatial multimode quantum information: modulation, detection and quantum correlations,” Phys. Rev. Lett. 98, 083602–1–083602–4 (2007).
[Crossref]
Weinreich, G.
P.A. Franken, A.E. Hill, C.W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]
Xie, X.
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
Yuan, X.
Compt. Rendue Acad. Sci. (1)
L.G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).
J. Appl. Phys. (1)
G.D. Boyd and D.A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys., 39, 3597–3639 (1968).
[Crossref]
J. of the Euro Opt. Soc.RP. (1)
M. Lassen, V. Delaubert, C.C. Harb, P.K. Lam, N. Treps, and HA. Bachor, “Generation of Squeezing in Higher Order HermiteGaussian Modes with an Optical Parametric Amplifier,” J. of the Euro Opt. Soc.RP. 1, 06003–1–06003–7 (2006).
J. Opt. Soc. Am (1)
R.W. Boyd, “Intuitive Explanation of the Phase Anomaly of Focused Light Beams,” J. Opt. Soc. Am 70, 877–880 (1980).
[Crossref]
J. Opt. Soc. Am. B (2)
J.T. Lue and C.J. Sun, “Limiting factors for parametric generation with focused highorder transverse and multilongitudinalmode lasers,” J. Opt. Soc. Am. B 4, 1958–1963 (1987).
[Crossref]
G. Breitenbach, S. Schiller, and J. Mlynek, “81% Conversion efficiency in frequencystable continuouswave parametric oscillation,” J. Opt. Soc. Am. B 12, 2095–2101 (1995).
[Crossref]
Jpn. J. Appl. Phys. (1)
T. Kasamatsu, H. Kubomura, and H Kan, “Numerical Simulation of Conversion Efficiency and Beam Quality Factor in Second Harmonic Generation with Diffraction and Pump Depletion,” Jpn. J. Appl. Phys., 44, 8495–8497 (2005).
[Crossref]
Opt. Express (1)
W.M. Lee, X. Yuan, and D. Tang, “Optical tweezers with multiple optical forces using doublehologram interference,” Opt. Express, 11, 199–207 (2002).
[Crossref]
Opt. Lett. (3)
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu, “Observation of a singlebeam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–291 (1986).
[Crossref]
[PubMed]
J.R. Kurz, J. Huang, X. Xie, T. Saida, and M.M. Fejer, “Mode multiplexing in optical f requency mixers,” Opt. Lett. 29, 551–553 (2004).
[Crossref]
[PubMed]
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Supplementary Material (1)
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Figures (8)
Scheme for single pass SHG measurement illustrated for the case of a TEM_{10} fundamental pump mode.
SHG efficiency as a function of the focusing parameter ξ, in optimal phase matching conditions, for i) TEM_{00}, ii) TEM_{10} and iii) TEM_{20} pump modes. All curves are normalized to the best conversion efficiency obtained for the TEM_{00} case. We have represented the three most relevant regimes to our analysis : ’thin crystal approximation regime’ corresponding to collimated beams, ’optimal focusing regime’, and ’tight focusing regime’. Two experimental points are represented in the optimal focusing region.
Modal decomposition of the SH field as a function of the focusing parameter ξ, in optimal phase matching conditions, for fundamental pump modes a) TEM_{10} and b) TEM_{20}. Traces i), ii) and iii) correspond to the TEM_{00}, TEM_{20} and TEM_{40} SH components, respectively. These results have been obtained with the analytical model.
Mode components of the SH fields as a function of the phase matching temperature, in optimum focusing conditions, for a) TEM_{10}3 and b) TEM_{20} pump modes. Traces i), ii) and iii) correspond to the TEM_{00}, TEM_{20} and TEM_{40} SH components, respectively. These results have been obtained with the analytical model.
Normalized temperature dependence of second harmonic conversion efficiency for pump modes a) TEM_{00}, b) TEM_{10} and c) TEM_{20}. The experimental data are represented by the black dots with indicative error bars. The solid lines are made with both theoretical models. The decomposition of the SH mode is also shown for each temperature with dotted/dashed lines. Traces i), ii) and iii) correspond to the TEM_{00}, TEM_{20} and TEM_{40} SH components, respectively. The maximum normalized theoretical conversion efficiency is 1 for a TEM_{00} pump, 0.50 for a TEM_{10} and 0.40 for a TEM_{20} pump mode. The pump beams were focused in all cases to a waist of
SH profiles generated in the crystal, observed in the far field (FF), for three different phase matching temperatures, with optimal focusing conditions, a) TEM_{10} and b) TEM_{20} pump modes. The crosssection traces contain both the experimental data and the theoretical fits. The length of the crystal was
This movie has been recorded with a CCD camera and shows the SH profiles generated by the nonlinear crystal. The phase matching temperatures is swept from below optimum phase matching to above optimum. The field is a TEM_{10} mode at 1064 nm and the SH filed moves from a predominantly TEM_{20} mode to a predominantly TEM_{00} mode. [
a)Illustration of a scheme for temperature sensing and control of a laser frequency over a wide spectrum. The beam is first converted into a desired higher order mode, in this case a TEM_{10} mode, with a modeconverter. Pumping the nonlinear material with this beam then generates a SH multimode beam. The detection of these modes requires spatial detectors like array or CCD detectors arrays or mode separator associated with individual detectors. b) Normalized SH mode amplitude difference dependence, ∆
Equations (4)
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